MHT CET 2021 22th September Evening Shift
Paper was held on Wed, Sep 22, 2021 8:30 AM
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Chemistry

Ethers when dissolved in cold concentrated sulphuric acid forms
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The volume of a gas at $$0^{\circ} \mathrm{C}$$ is $$2 \mathrm{~dm}^3$$. What is its volume if temperature is decreased
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The major product obtained in the following reaction is Chlorobenzene + chlorine $$\xrightarrow[\mathrm{FeCl}_3]{\text {
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How many moles of urea are present in 5.4 g ? (Molar mass = 60)
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Which among the following is a double ring containing nitrogen base present in nucleic acids?
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Identify the product '$$\mathrm{B}$$' in the following series of reactions. $$\text { Propan - 1-ol } \xrightarrow[623 \
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Conversion of benzene diazonium chloride to chlorobenzene in presence of $$\mathrm{CuCl} / \mathrm{HCl}$$ is known as
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Which among the following compounds in NOT a colourless gas?
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Solubility product of $$\mathrm{AgBr}$$ is $$4.9 \times 10^{-13}$$. What is its solubility?
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Which element from following is radioactive?
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Which among the following statements about $$\left[\mathrm{Ni}(\mathrm{CN})_4\right]^{2-}$$ is $$\underline{\text { NOT
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Formation of $$\mathrm{NO}_{2(\mathrm{g})}$$ from $$\mathrm{N}_{2(\mathrm{g})}$$ and $$\mathrm{O}_{2(\mathrm{g})}$$ is a
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Identify reducing agent in following reaction $$\mathrm{H}_2 \mathrm{O}_{2(\mathrm{ag})}+\mathrm{ClO}_{4(\mathrm{aq})}^{
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Identify the type of unit cell that has particles at the centre of each face in addition to the particles at eight corne
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Identify product '$$\mathrm{B}$$' in following reaction. Cumene $$\xrightarrow[\Delta]{\mathrm{KMnO}_4, \mathrm{KOH}} \m
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Which of the following is NOT a correct mathematical equation for Ostwald dilution law?
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How many Faraday of electricity is required to deposit $$0.8 \mathrm{~g}$$ of calcium at cathode by the electrolysis of
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Identify lowest positive charge developed (indicated by $$\partial, \partial_1, \partial_2, \partial_3$$) due to inducti
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What is rate constant of a first order reaction if 0.08 mole of reactant reduces to 0.02 mole in 23.03 minute?
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Which element from following lanthanoids has half-filled $$\mathrm{f}$$- orbital in observed and expected electronic con
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How many atoms of niobium are present in $$2.43 \mathrm{~g}$$ if it forms bcc structure with density $$9 \mathrm{~g} \ma
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Identify the reagent R used in following conversion. Glucose $$\mathrm{\buildrel R \over \longrightarrow}$$ n - hexane
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Buna-S is obtained from
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5 g sucrose (molar mass = 342) is dissolved in 100 g of solvent, decreases the freezing point by 2.15 K. What is cryosco
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What is Henry's law constant if solubility of a gas in water at $$298 \mathrm{~K}$$ and 1 bar pressure is $$7\times10^{-
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A weak monobasic acid is $$10 \%$$ dissociated in $$0.05 \mathrm{~M}$$ solution. What is its percentage dissociation in
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What is the conductivity of $$0.02 \mathrm{~M} \mathrm{~KCl}$$ solution if cell constant is $$1.29 \mathrm{~cm}^{-1}$$ w
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The major product obtained in the following reaction is
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Which of the following statements is NOT true for a reaction having rate law $$\mathrm{r}=\mathrm{k}\left[\mathrm{H}_2\r
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Identify the product '$$B$$' in following reaction. $$2 \mathrm{CH}_3 \mathrm{CHO} \xrightarrow{\text { dil. } \mathrm{N
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Identify the correct decreasing order of precipitation power of flocculating ion added, from following.
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Identify use of argon from following.
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Which of the following is an example of copolymer?
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Which of the following is likely to undergo racemization during alkaline hydrolysis?
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What is enthalpy of formation of $$\mathrm{NH}_3$$ if bond enthalpies are as $$(\mathrm{N} \equiv \mathrm{N})=941 \mathr
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Which of the following alkyl halide is treated with sodium metal to obtain $$2,2,3,3$$ - tetramethyl butane?
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Electrical conductance due to all the ions in $$1 \mathrm{~cm}^3$$ of given solution is called as
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For the reaction $$\mathrm{N}_{2(\mathrm{~g})}+3 \mathrm{H}_{2(\mathrm{~g})} \rightarrow 2 \mathrm{NH}_{3(\mathrm{~g})}$
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Identify the polymer used in making floor tiles.
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Which of the following formulae is used to obtain depression in freezing point?
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How many tetrahedral voids are present in 0.4 mole of a compound that forms hcp structure?
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Pure dihydrogen $$(99.5 \%)$$ is obtained by the electrolysis of
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Which among following functional groups exhibits $$-\mathrm{R}$$ effect?
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Which among the following compounds has highest melting point?
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Identify compound from following having highest basic strength.
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Which of the following alkenes on oxidation by $$\mathrm{KMnO}_4$$ in dil. $$\mathrm{H}_2 \mathrm{SO}_4$$ forms adipic a
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What is the difference between $$\Delta H$$ and $$\Delta \mathrm{U}$$ for reaction given below at $$298 \mathrm{~K}$$ ?
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What is the energy of an electron in stationary state corresponding to $$\mathrm{n}=2$$ ?
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Identify the molecule having dipole moment.
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Identify homoleptic complex from following.
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Mathematics

Let $$\begin{aligned} f(x) & =x+a \sqrt{2} \sin x & & , 0 \leq x If $$\mathrm{f}(\mathrm{x})$$ is continuous for $$0 \le
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The area of triangle with vertices $$(1,2,0),(1,0, a)$$ and $$(0,3,1)$$ is $$\sqrt{6}$$ sq. units, then the values of '$
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If $$A=\left[\begin{array}{cc}5 a & -b \\ 3 & 2\end{array}\right]$$ and $$A$$ adj $$A=A A^T$$, then $$5 a+b=$$
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The numbers can be formed using the digits $$1,2,3,4,3,2,1$$ so that odd digits always occupy odd places in __________ w
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If $$y=\tan ^{-1} \sqrt{\frac{1+\cos x}{1-\cos x}}$$, then $$\frac{d y}{d x}=$$
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Following data shows the information about marks obtained in Physics, Chemistry, Mathematics and Biology by 100 students
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If $$\mathrm{G}(4,3,3)$$ is the centroid of the triangle $$\mathrm{ABC}$$ whose vertices are $$\mathrm{A}(\mathrm{a}, 3,
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The d.r.s. of the normal to the plane passing through the origin and the line of intersection of the planes $$x+2 y+3 z=
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The degree of the differential equation whose solution is $$y^2=8 a(x+a)$$, is
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If the sum of slopes of lines represented by $$\mathrm{ax^2+8xy+5y^2=0}$$ is twice their product, then a =
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In $$\Delta ABC$$, with usual notations $$\mathrm{\frac{b\sin B-c\sin C}{\sin(B-C)}}=$$
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Two circles centred at $$(2,3)$$ and $$(4,5)$$ intersects each other. If their radii are equal, then the equation of the
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The function $$f(x)=\frac{\lambda \sin x+6 \cos x}{2 \sin x+3 \cos x}$$ is increasing, if
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If $$f(x)=x^2+a x+b$$ has minima at $$x=3$$ whose value is 5 , then the values of $$a$$ and $$b$$ are respectively.
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The area bounded by the parabola $$y^2=x$$ and the line $$x+y=2$$ in the first quadrant is
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If $$2 \cos \theta=x+\frac{1}{x}$$, then $$2 \cos 3 \theta=$$
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For an invertible matrix $$A$$, if $$A(\operatorname{adj} A)=\left[\begin{array}{cc}20 & 0 \\ 0 & 20\end{array}\right]$$
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$$\int_\limits{\frac{\pi}{6}}^{\frac{\pi}{2}} \frac{\operatorname{cosec} x \cdot \cot x}{1+\operatorname{cosec}^2 x} d x
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A spherical raindrop evaporates at a rate proportional to its surface area. If its radius originally is 3 mm. and 1 hour
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The differential equation of all parabolas having vertex at the origin and axis along positive Y-axis is
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If the vectors $$2 \hat{i}-\hat{j}-\hat{k} ; \hat{i}+2 \hat{j}-3 \hat{k}$$ and $$3 \hat{i}+\lambda \hat{j}+5 \hat{k}$$ a
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$$\lim _\limits{x \rightarrow 2}(x-1)^{ \frac{1}{3 x-6}}=$$
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Given $$\mathrm{p}$$ : A man is a judge, $$\mathrm{q}$$ : A man is honest If $$\mathrm{S} 1$$ : If a man is a judge, the
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If $$2 \tan ^{-1}(\cos x)=\tan ^{-1}(2 \operatorname{cosec} x)$$, then the value of $$x$$ is
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$$\int \frac{\tan ^4 \sqrt{x} \cdot \sec ^2 \sqrt{x}}{\sqrt{x}} d x=$$
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The line $$\frac{x-2}{3}=\frac{y-1}{-5}=\frac{z+2}{2}$$ lies in the plane $$x+3 y-\alpha z+\beta=0$$, then value of $$\a
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The statement pattern $$(p \wedge q) \wedge[(p \wedge q) \vee(\sim p \wedge q)]$$ is equivalent to
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If the points $$P(4,5, x), Q(3, y, 4)$$ and $$R(5,8,0)$$ are collinear, then the value of $$x+y$$ is
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The particular solution of the differential equation $$\frac{d y}{d x}=\frac{y+1}{x^2-x}$$, when $$x=2$$ and $$y=1$$ is
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The distribution function $$F(X)$$ of discrete random variable $$X$$ is given by .tg {border-collapse:collapse;border-
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The general solution of $$\frac{d y}{d x}=\frac{x+y}{x-y}$$ is
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A line drawn from a point $$A(-2,-2,3)$$ and parallel to the line $$\frac{x}{-2}=\frac{y}{2}=\frac{z}{-1}$$ meets the $$
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First bag contains 3 red and 5 black balls and second bag contains 6 red and 4 black balls. A ball is drawn from each ba
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If $$A=\left[\begin{array}{ccc}1 & 2 & 1 \\ -1 & 1 & 3\end{array}\right]$$ and $$B=\left[\begin{array}{cc}1 & 2 \\ -3 &
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With usual notations, in any $$\triangle A B C$$, if $$a\cos B=b \cos A$$, then the triangle is
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A fair coin is tossed 4 times. If $$X$$ is a random variable which indicates number of heads, then $$\mathrm{P}[\mathrm{
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If the line joining two points $$\mathrm{A}(2,0)$$ and $$\mathrm{B}(3,1)$$ is rotated about $$\mathrm{A}$$ in anticlockw
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The common region of the solution of the inequations $$x+y \geq 5, y \leq 4, x \geq 2, x, y \geq 0$$ is
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If the mean and variance of a binomial distribution are 4 and 2 respectively, then probability of getting 2 heads is
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The vector equation of the line whose Cartesian equations are $$y=2$$ and $$4 x-3 z+5=0$$ is
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If $$x^y \cdot y^x=16$$, then $\frac{d y}{d x}$ at $(2,2)$$ is
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$$\int_\limits0^2|2 x-3| d x=$$
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$$\int \cos ^{-1} x d x=$$
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$$\int \frac{1}{\cos x+\sqrt{3} \sin x} d x=$$
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If $$f(x)=[8 x]-3$$, where $$[x]$$ is greatest integer function of $$x$$, then $$f(\pi)=$$ (where $$\pi=3,14$$)
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If lines represented by the equation $$\mathrm{px}^2-\mathrm{qy^{2 }}=0$$ are distinct, then
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The slant height of a right circular cone is $$3 \mathrm{~cm}$$. The height of the cone for maximum volume is
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If $$\omega$$ is the complex cube root of unity, then $$\left(3+5 \omega+3 \omega^2\right)^2+\left(3+3 \omega+5 \omega^2
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Let $$a: \sim(p \wedge \sim r) \vee(\sim q \vee s)$$ and $$b:(p \vee s) \leftrightarrow(q \wedge r)$$. If the truth valu
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If $$\int_\limits0^a \sqrt{\frac{a-x}{x}} d x=\frac{k}{2}$$, then $$k=$$
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Physics

Force is applied to a body of mass $$2 \mathrm{~kg}$$ at rest on a frictionless horizontal surface as shown in the force
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Which of the following gates will give an output '1' for the given inputs?
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For a common-emitter amplifier, the voltage gain is 40. Its input and output impedances are $$100 \Omega$$ and $$400 \Om
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A tuning fork of frequency '$$n$$' is held near the open end of tube which is closed at the other end and the lengths ar
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In parallel plate capacitor, electric field between the plates is '$$E$$'. If the charge on the plates is '$$Q$$' then t
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A particle with position vector $$\overrightarrow{\mathrm{r}}$$ has a linear momentum $$\overrightarrow{\mathrm{P}}$$. W
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A ball rises to the surface of a liquid with constant velocity. The density of the liquid is four times the density of t
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A particle having a charge $$100 \mathrm{e}$$ is revolving in a circular path of radius $$0.8 \mathrm{~m}$$ with 1. r.p.
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Two satellites of same mass are launched in circular orbits at heights '$$R$$' and '$$2 R$$' above the surface of the ea
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The emissive power of sphere of area $$0.04 \mathrm{~m}^2$$ is $$0.7 \mathrm{~k} \mathrm{~cal} \mathrm{~s}^{-1} \mathrm{
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In a potentiometer experiment, the balancing length for a cell is $$240 \mathrm{~cm}$$. On shunting the cell with a resi
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A sound wave of frequency $$160 \mathrm{~Hz}$$ has a velocity of $$320 \mathrm{~m} / \mathrm{s}$$. When it travels throu
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In $$n^{\text {th }}$$ Bohr orbit, the ratio of the kinetic energy of an electron to the total energy of it, is
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Two spherical conductors of radii $$4 \mathrm{~cm}$$ and $$5 \mathrm{~cm}$$ are charged to the same potential. If '$$\si
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Kirchhoff's current and voltage law are respectively based on the conservation of
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A glass tube of $$1 \mathrm{~m}$$ length is filled with water. The water can be drained out slowly from the bottom of th
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The rate of flow of heat through a copper rod with temperature difference $$28^{\circ} \mathrm{C}$$ is $$1400 \mathrm{~c
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A capacitor of capacity '$$C$$' is charged to a potential '$$V$$'. It is connected in parallel to an inductor of inducta
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When a photon enters glass from air, which one of the following quantity does not change?
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In Young's double slit experiment using monochromatic light of wavelength '$$\lambda$$', the maximum intensity of light
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An electron of mass '$$m$$' and charge '$$q$$' is accelerated from rest in a uniform electric field of strength '$$E$$'.
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If the terminal speed of a sphere A [density $$\rho_{\mathrm{A}}=7.5 \mathrm{~kg} \mathrm{~m}^{-3}$$ ] is $$0.4 \mathrm{
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A particle connected to the end of a spring executes S.H.M. with period '$$T_1$$'. While the corresponding period for an
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The change in internal energy of the mass of a gas, when the volume changes from '$$\mathrm{V}$$' to '$$2 \mathrm{~V}$$'
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An object is located on a wall, its image of equal size is to be obtained on a parallel wall with the help of a convex l
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A child is standing with folded hands at the centre of the platform rotating about its central axis. The kinetic energy
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If the pressure of an ideal gas is decreased by $$10 \%$$ isothermally, then its volume will
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The critical angle for light going from medium '$$x$$' to medium '$$Y$$' is $$\theta$$. The speed of light in medium '$$
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A needle is $$7 \mathrm{~cm}$$ long. Assuming that the needle is not wetted by water, what is the weight of the needle,
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A driver applies the brakes on seeing the red traffic signal $$400 \mathrm{~m}$$ ahead. At the time of applying the brak
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An ideal gas having molar mass '$$\mathrm{M}_0$$', has r.m.s. velocity 'V' at temperature 'T'. Then
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A step down transformer is used to reduce the main supply from '$$V_1$$' volt to '$$V_2$$' volt. The primary coil draws
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For the circuit shown below, instantaneous current through inductor '$$\mathrm{L}$$' and capacitor '$$\mathrm{C}$$' is r
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The light of wavelength '$$\lambda$$' is incident on the surface of metal of work function $$\phi$$ and emits the electr
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A parallel plate capacitor having plates of radius 6 cm has capacitance 100 pF. It is connected to 230 V a.c. supply wit
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At a height 'R' above the earth's surface the gravitational acceleration is (R = radius of earth, g = acceleration due t
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Two rings of radius 'R' and 'nR' made of same material have the ratio of moment of inertia about an axis passing through
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'$$n$$' waves are produced on a string in 1 second. When the radius of the string is doubled, keeping tension same, the
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the magnetic flux (in weber) in a closed circuit of resistance $$20 \Omega$$ varies with time $$t$$ second according to
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If '$$E$$' and '$$L$$' denote the magnitude of total energy and angular momentum of revolving electron in $$\mathrm{n}^{
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The magnetic field inside a current carrying toroidal solenoid is $$0.2 \mathrm{~mT}$$. What is the magnetic field insid
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A body of mass '$$m$$' performs linear S.H.M. given by equation $$x=P \sin \omega t+Q \sin \left(\omega t+\frac{\pi}{2}\
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Two particles $$A$$ and $$B$$ having same mass have charge $$+q$$ and $$+4 q$$ respectively. When they are allowed to fa
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The relative permeability of iron is 2000. Its absolute permeability in SI unit will be $$\left(\frac{\mu_0}{4 \pi}=10^{
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Choose the correct statement. In semiconductors valance band and conduction band
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A step down transformer has turns ratio $$20: 1$$. If $$8 \mathrm{~V}$$ is applied across $$0.4 \mathrm{~ohm}$$ secondar
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Photons of energy $$10 \mathrm{~eV}$$ are incident on a photosensitive surface of threshold frequency $$2 \times 10^{15}
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Two radioactive materials $$X_1$$ and $$X_2$$ have decay constants '$$5 \lambda$$' and '$$\lambda$$' respectively. Initi
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If two sources emit light waves of different amplitudes then
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An ideal gas at $$27^{\circ} \mathrm{C}$$ is compressed adiabatically to $$(8 / 27)$$ of its original volume. If ratio o
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